Well, having traveled it, I know the answer:
In terms of your life and the knowledge you will ever know - it is infinite. In mathematical terms, it is finite. In relative terms, it is infinite. In terms of the human imagination, it is finite.
The human mind is expansionless, but try to imagine "nothing". That is what exists "outside" the Universe. Try this: ever look at a vaccum tube made of glass. You know nothing is "in there", but your mind says, "how can it be empty". There 'has' to be something in there. Some air or some molecules. Nope, it is a vaccum.
Therefore, the Universe. It is infinitely finite. (just kidding)
On the other hand, modern physicists are arguing over the age, size, shape and mass of the Universe. It will be hard to pinpoint these, until we have stopped discovering new things like blackholes, dark matter, strings and neutrinos.
So, the answer to your question is like a two sided coin:
Side 1] the Universe is infinite. It goes on and on and on, neverending. This believe will keep your imagination running wild with theories.
Side 2] the Universe is finite. It has bounds, which define matter and nothing. Outside the Universe is vast emptiness. Inside are galaxies, stars, mega-gas and dust clouds, and so on. It could be round, doughnut, or flat in shape.
I believe it is basically finite in nature. Outside it is nothing, expect maybe other instances of Universes. It will never matter to me, so I don't stress over it much. I guess, for now, I will just continue to mix my belief with that of the like of Steven Hawkings who believes it is "finite"
More info: http://www.hawking.org.uk/lectures/lindex.html
-my two cents